CAJ | 학술논문

本文研究了平面正方形区域上不可压缩的Navier-Stokes方程五模类Lorenz方程组的混沌行为问题.利用傅立叶展开方法对Navier-Stokes方程进行模式截断,获得了新五模类Lorenz方程组,给出了该方程组定常解及其稳定性的讨论,证明了该方程组吸引子的存在性,并对其全局稳定性进行了分析和讨论.
본문연구료평면정방형구역상불가압축적Navier-Stokes방정오모류Lorenz방정조적혼돈행위문제.이용부립협전개방법대Navier-Stokes방정진행모식절단,획득료신오모류Lorenz방정조,급출료해방정조정상해급기은정성적토론,증명료해방정조흡인자적존재성,병대기전국은정성진행료분석화토론.
In this article,we study the dynamical behavior of a five-mode Lorenz system of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus.First,we derive amodel system by taking five modes in the Fourier expansion of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus,and then discuss the stability of stationary points of the five-mode system.Secondly,we prove the existence of its attractor,and discuss the global stability of the system.